# harmonic

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## harmonic.

**1**Physical term describing the vibration

**vibration,**

in physics, commonly an oscillatory motion—a movement first in one direction and then back again in the opposite direction. It is exhibited, for example, by a swinging pendulum, by the prongs of a tuning fork that has been struck, or by the string of a musical

**.....**Click the link for more information. in segments of a sound-producing body (see sound

**sound,**

any disturbance that travels through an elastic medium such as air, ground, or water to be heard by the human ear. When a body vibrates, or moves back and forth (see vibration), the oscillation causes a periodic disturbance of the surrounding air or other medium that

**.....**Click the link for more information. ). A string vibrates simultaneously in its whole length and in segments of halves, thirds, fourths, etc. These segments form what is known in algebra as a harmonic series or progression, since the rate of vibration of each segment is an integral multiple of the frequency of the whole string, i.e., each segment vibrates respectively twice, three times, four times, etc., as fast as the whole string. The vibration of the whole string produces the fundamental tone, and the segments produce weaker subsidiary tones. A similar phenomenon occurs in an air column in a pipe. At most the first 16 tones in such a series can be heard by the human ear; the character or timbre of a fundamental tone is determined by the number of its subsidiary tones heard and their relative intensity. The subsidiary tones have been loosely called harmonics (as a noun), but they are properly called partials, the fundamental tone being the first partial. They are also called overtones (a synonym for "upper partials"), although this term includes a number of sounds that do not fit in with the harmonic series, and are therefore not considered musical.

**2**Term describing the silvery sound produced separately when the fundamental and possibly more partial tones are damped by touching a string at a nodal point. Similarly harmonics are produced separately in an air column by overblowing or in brass wind instruments by the use of valves.

## Harmonic (periodic phenomena)

A sinusoidal quantity having a frequency that is an integral multiple of the frequency of a periodic quantity to which it is related. *See* Mode of vibration

A harmonic series of sounds is one in which the basic frequency of each sound is an integral multiple of some fundamental frequency. The name exists for historical reasons, even though according to the usual mathematical definition such frequencies form an arithmetic series. An ideal string (or air column) can vibrate as a whole or in a number of equal parts, and the respective periods of vibration are proportional to the lengths. These increasingly shorter lengths or periods form a harmonic series. The name came from the harmonious relation of such sounds, and the science of musical acoustics was once called harmonics. Nowadays, it is customary to deal with ratios of frequency rather than ratios of length and, because frequency is the reciprocal of period, the definition of harmonic in acoustics becomes that given here. *See* Musical acoustics

## harmonic

[här′män·ik]## harmonic

## harmonic

## harmonic

**1.**

*Music*of, relating to, or belonging to harmony

**2.**

*Maths*

**a.**capable of expression in the form of sine and cosine functions

**b.**of or relating to numbers whose reciprocals form an arithmetic progression

**3.**

*Physics*of or concerned with an oscillation that has a frequency that is an integral multiple of a fundamental frequency

**4.**

*Physics*

*Music*a component of a periodic quantity, such as a musical tone, with a frequency that is an integral multiple of the fundamental frequency. The

**first harmonic**is the fundamental, the

**second harmonic**(twice the fundamental frequency) is the

**first overtone**, the

**third harmonic**(three times the fundamental frequency) is the

**second overtone,**etc.

**5.**

*Music*(not in technical use) overtone: in this case, the first overtone is the first harmonic, etc.